for all \(l = 1,\ldots ,L_{\max },\ L =L 1,\ldots ,L_{\max }\) . Hence, it follows from Corollary 6.4 in [1]} (see also Theorem 1 in [2]}) that there exist constants \(C_1,C_2 > 0\)  (not depending on \(L\) ) such that for any \(t > 0\) ,
\(\mathbb {P}\left( \left. \sum _{l = 1}^{L_{\max }} \left(\tau _{L,l,e} - \tau _{L,l,s} \right)^{-1} \left(\sum _{j = \tau _{L,l,s} + 1}^{\tau _{L,l,e}} Y_{nj}\right)^2 \ge C_1 \sqrt{L_{\max } t} + C_2 t^2 \right|\mathcal {T}_L \right) \le 2 e^{-t}\) 
